PGroupRank - Maple Help
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GroupTheory

 PGroupRank
 determine the rank of a group of prime power order

 Calling Sequence PGroupRank( G )

Parameters

 G - a permutation group

Description

 • The rank of a finite $p$-group $G$, where $p$ is a prime number, is the minimum number of generators of $G$.
 • The PGroupRank( G ) command returns the rank of the finite $p$-group G, which must be an instance of a permutation group.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{DihedralGroup}\left(8\right)$
 ${G}{≔}{{\mathbf{D}}}_{{8}}$ (1)
 > $\mathrm{PGroupRank}\left(G\right)$
 ${2}$ (2)
 > $\mathrm{PGroupRank}\left(\mathrm{QuaternionGroup}\left(4\right)\right)$
 ${2}$ (3)
 > $\mathrm{PGroupRank}\left(\mathrm{WreathProduct}\left(\mathrm{QuaternionGroup}\left(\right),\mathrm{CyclicGroup}\left(4\right)\right)\right)$
 ${3}$ (4)
 > $\mathrm{PGroupRank}\left(\mathrm{ElementaryGroup}\left(5,5\right)\right)$
 ${5}$ (5)